Stephen Hester, the chief executive of Royal Bank of Scotland, was forced to issue a public apology after the bank was unable to say how much longer it would take to clear the backlog of payments for hundreds of thousands of NatWest customers affected by a computer glitch.

"Our customers rely on us day in and day out to get things right, and on this occasion we have let them down," Hester said. "This should not have happened."

Amid rising anger, he had spent Saturdayat RBS's City headquarters overseeing efforts to process the mountain of transactions delayed by the IT problem, which began on Thursday. In total, 7,000 staff were coming in on Sundayto handle customers' queries and tackle the backlog.

RBS said the technical hitch which caused the problem had been "identified and corrected", but when asked whether the issues could continue, a spokesman said: "We can't rule it out."

In a separate message to his staff, Hester, who waived a £963,000 bonus earlier this year after a public outcry, said: "I know we're not out of the woods yet and there is more hard work ahead. You have my support."

NatWest, which is owned by RBS, extended the opening hours of 900 branches on Saturday to allow affected customers access to their cash, and will open them again today. Customers at Ulster Bank, part of the RBS group, have also been hit.

People who could show they should have received payments were offered emergency cash payouts to tide them over. "Where our customers are facing hardship or difficulty, we can and will help them," Hester said.

The bank has also been forced to promise redress to thousands of other people, many not NatWest customers, who have failed to receive their salaries because their employers use the bank.

The RBS spokesman said the bank would refund overdraft charges or other costs incurred by customers who have slipped into the red or seen direct debits bounce as a result of the problems.

Louis Brook, of the Move Your Money campaign, which urges the public to switch from the big high-street banks to ethical or mutual lenders, said he expected a surge in support from disgruntled NatWest customers.

"People are incredibly loyal and have quite strong emotional attachments to their banks, but when that's broken by something so fundamental as not being able to get access to your own money, it can be the last straw," he said.